There's actually two problems here. The first thing I noticed was that it was telling me to Set executable permissions for the gradle binary it just downloaded/unzipped. I figured I might just need to re-run the command with sudo.

After following the Getting Started guide, creating a simple project via the command flixel tpl -n "HelloWorld",.and then setting up Android via the lime setup android command, as per the Android guide, I still could not build for Android via the command lime build android, because I would get the following error message: